function vf_out4 = fn_an(n, vx, vf, vx_out)

vf_out4 = zeros(1, length(vx_out));

for i = 1:length(vx_out)
    
   k = vx_out(i);
   vf_out4(i) = fn_int_an(n, vx, vf, k);
    
end

end